\(H^p \rightarrow L^p\) Boundedness of Fourier Multipliers on Graded Lie Groups

In this contribution, we discuss the joint work with Hong et al. (Fourier multipliers for Hardy spaces on graded Lie groups. In: Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 153(5), 1729–1750, 2022. https://doi.org/10.1017/prm.2022.71 ) wherein we have investigated the \(H^p(G) \rightarrow L^p(G)\) , \(0< p \leq 1\) , boundedness of Fourier multiplier operators on an arbitrary graded Lie group G, where \(H^p(G)\) is the Hardy spaces on G. Our main result extends those obtained by Fischer and Ruzhansky (Colloq Math 165:1–30, 2021), who proved the \(L^1(G)\rightarrow L^{1,\infty }(G)\) and \(L^p(G) \rightarrow L^p(G)\) , \(1< p <\infty \) , boundedness of such Fourier multiplier operators.